Polymerized spacetime dynamics with multi-field source: unraveling the pre-inflationary Universe

We study a multi-field model in Loop Quantum Cosmology for a maximally symmetric spacetime governed by the Einstein–Hilbert action minimally coupled to scalar fields. Using a Legendre transformation, we formulate the Hamiltonian dynamics in canonically equivalent geometrodynamical and Yang–Mills–type representations, incorporating nontrivial couplings through a geometric structure on the multi-field configuration space. Implementing the $\bar{\mu }$-scheme polymerization, we obtain the loop-quantum-corrected Friedmann equations. By focusing on the two-field model as an example, we analyze the effective dynamics for specific potentials. The $\mathit{\text{quantum}}\mathit{\text{bouncing,}}\mathit{\text{transition,}}\mathit{\text{and}}\mathit{\text{slow-roll}}\mathit{\text{inflationary}}$ phases are investigated numerically, and viability of the models is assessed by evaluating the number of e-folds during the inflationary phase for certain given initial conditions. The global behavior of the background evolution is further examined through linear stability and dynamical-systems analyses.